mK_4的点可区别全染色

Vertex-Distinguishing Total Colorings of mK_4

利用色集事先分配法,借助于矩阵构造具体染色及递归法的方法,研究图的点可区别全染色问题,给出了m个K4的点不交的并mK4的点可区别全色数χvt(mK4)的确切值,即"如果(k-1)4<4m≤(k)4,m≥2,k≥6,则χvt(mK4)=k".验证了VDTC猜想对mK4成立.

The problem of vertex-distinguishing total colorings of graphs was discussed via the methods of distributing color sets in advance, constructing concrete coloring with the help of matrices and recurrence method. The exact value of the vertex-distinguishing total chromatic number y. （mK.） of the. nninn inK. n mvertex-disjoint K4 was given, that is ＂If（k-1 4）〈4m≤（k 4）,m≥2,k≥6,则Xm（mK4）=K＂Thisillustrates that the VDTC conjecture is valid for mK4.